In defence of shameless self-promotion

[Interaxus]

‘Promulgatio sui improba’ can be a good thing sometimes. Without Adriani shameless self-promotion and accompanying link to the abacus lesson
(http://www.youtube.com/adrianmallon) I would have missed one of the best Latin lessons I've ever had. Kudos, mi Adriane! If only I’d been taught maths like that in school ...

The reading from the Aeneid was also enjoyable to listen to (though ‘Musa, mihi cauzas memora' jarred slightly). Who was reading?

The animated mouth was less successful. Scary in fact. A bit of shadow on those dazzling dentures might help. But I realize it’s just a matter of time before the technology catches up with the dream.

Good luck with the (perhaps shamelessly ambitious) project!

Cheers,
Int

[adrianus]

Thanks, Interaxus, for the kind words. I know there are mistakes in pronunciation in the videos and I point out some in the text accompanying them. Additionally and most welcomely, Avitus pointed out that my "-io" word endings are properly two syllables. I deliberately was pronouncing "-io" as "-yo" because I thought it was legitimate in common speech but I must be wrong. And he told me my centum mīlia should be centēna mīlia, not quīngenta mīlia but quīnquiēs centēna mīlia, and not mīliō but deciēs centēna mīlia. So if you see more mistakes, attach comments to the YouTube videos or here. I published the videos not to instruct for the meantime but for feedback. http://www.youtube.com/adrianmallon

Oh, and I'm the one speaking the lines of the Aeneid. There are mistakes, but on elision note that I was speaking without elision deliberately to see how it sounded, not to recommend it.

Gratias de verbis benevolis tibi ago, Interaxe. Scio in taeniolis verba quae malè sono esse, et expositionibus adsequentibus quas correctiones do. Avitus mihi dixit me non propriè "io" terminantem duabus syllabis enuntiasse, quae critica mihi gratissima et necessaria est. Id consultò feci quòd sic licere loquelâ imaginatus sum at malè, ut videtur. Porrò is haec errata indicavit: non centum mīlia sed centēna mīlia, non quīngenta mīlia sed quīnquiēs centēna mīlia, non mīliō sed deciēs centēna mīlia. Dein si quis plura videat, is vel in YouTube vel hûc commentationes ad taeniolas affingat. Taeniolas interim exposui ut corrigantur, non ut erudiam.

Ego sum qui versus Aeneidos recito. Item erravi a hoc nota: elisionem in loquendi omissi ut experientiam tentarim, non ut probarem.

[adrianus]

I'm not able to add comments to my own video, it seems, in the absence of another commenting, so please add a comment on YouTube to the abacus video giving Avitus's corrections or other corrections, if that's OK.

Commentarios taeniolis propriis meis addere non queo, ut videtur, sine priùs alius annotet. Deinde, te amabò, corrigenda Aviti vel alia taeniolae abaci in YouTube addas, si tibi non molestum sit.

[adrianus]

Avitus pointed out that my "-io" word endings are properly two syllables. I deliberately was pronouncing "-io" as "-yo" because I thought it was legitimate in common speech but I must be wrong.

Isn't terminal "-io" just one syllable in the Aeneid, or is that beside the point?
Nonnè in Aeneide una syllaba simpliciter est "-io" terminans, aut an id rem non spectat?

[Alatius]

Isn't terminal "-io" just one syllable in the Aeneid, or is that beside the point?

Hm, I don't think I have heard anything about that, nor do I see any evidence for it when I look through the text. For example, these are the -io endings from book I:

Latio genus
excidio Libyaa
Latio multosque
imperio premit
conubio iungam
seditio saevitque
Trinacrio dederatque
Latio regnantem
imperio explebit
servitio premet
hospitio Teucris
remigio alarum
medio sic
nuntio et in tutum
regio in terris
Dardanio Aeneae
parce pio generi
Hospitio prohibemur
officio nec te
auxilio tutos
medio in fluctu
Dardanio Anchisae
auxilio Beli
Ascanio ferat
Ascanio cari
Ascanio veniat
confugio et supplex
gremio accipiet
Ascanio placidam
gremio dea
gremio fovet
vario noctem

Most follow the pattern of "Lătiō genus": the syllable before -io is short, and the -ō is not elided. Of course, it is possible to read this as "Latjō genus", with the preceding syllable long by position. But if the ending is regularly -jō, then we would expect also cases were the preceding syllable is long regardless of the j, right? However, it is almost always short, with an exception in verse 391:
nuntio et in tutum versis aquilonibus actam
But the straightforward scanning here is nun-tĭ-e-tin-tu-..., with the "trapped" ĭ saved by elision of the ō. I think that is vastly preferable to the alternative, nun-tjŏ-e-tin-tu-, with a shortened -ō.

[adrianus]

But if the ending is regularly -jō, then we would expect also cases were the preceding syllable is long regardless of the j, right? However, it is almost always short, with an exception in verse 391:

Thanks, Alatius. You're right, of course. I must have read something about this and, by trying to be too clever. let a distant memory muddle me.

Gratias, Alati. Rectus es, nunc non dubito. Quoddam de hâc re legerim quod malè in memoriae repetendo me confudit qui callidiorem esse voluissem.

[adrianus]

But the straightforward scanning here is nun-tĭ-e-tin-tu-..., with the "trapped" ĭ saved by elision of the ō. I think that is vastly preferable to the alternative, nun-tjŏ-e-tin-tu-, with a shortened -ō.

Wait. I reread more carefully what you said. I have heard others eliding that way and I don't think it's right. Long doesn't become short by elision. Long remains long by elision. Surely "-ō ě-" becomes "-ō-" not "-ě-", so isn't the preferred scansion "nun-tjō-tin"? After all, "nuntiet" is present active subjunctive and a different person!

Mane! Cautiùs quod dixisti perlegi. Alios audivi qui similiter elidunt at malè, ut opinor. Nonnè longa restat vocalis quae aliam brevem elidit? Nonnè "nun-tjō-tin" dicamus? Tempore praesenti vocis activae modo subjunctivo et aliae personae est enim "nuntiet".

[adrianus]

See also Book X, line 904.
Vide etiam liber decimus, versus nongenti quattuor.

corpus humō patiāre tegī. Sciō acerba meōrum
corpus hu-|-mō pati-|-āre te-|-gī. Sciō a-|-cerba me-|-ōrum

Here also, I reckon, "-io" is "-jo" or "scĭō ă-" = "scjō-"
Et hîc non "scĭ ă-" sed "scjō-" legendum est, ut puto.

Book XI, line 31.
Liber undecimus, versus triginta unus

servābat sēnior, quī Parrhasiō Ēvandrō
servā-|-bat sen-|-jor, quī| Parrhas-|jō Ē-|-vandrō
or // aut
servā-|-bat seni-|-or, quī| Parrhasi-|-ō Ē-|-vandrō

I prefer the first. // Primum praefero.

Corrigendum

quō gemi-|-tū con-|-versī ani-|-mī com-|-pressus e-|t omnis

Immō age e-|-t...

Ah! I was wrong about long not becoming short. Here it does. Then I'm wrong about everything.
De hâc re erravi: longa elisione brevem benè fieri potest, sicut itá. Deinde de omnibus erro.

[adrianus]

And he told me my centum mīlia should be centēna mīlia, not quīngenta mīlia but quīnquiēs centēna mīlia, and not mīliō but deciēs centēna mīlia

I checked and "centum mīlia", "quīngenta mīlia" and "mīliō" are correct as cardinals (the last is neo-Latin, mind you), while "centēna mīlia", "quīnquiēs centēna mīlia", "deciēs centēna mīlia" apply as distributives and numeral adverbs, not cardinals. (See refs. given below.) But should I properly count as the Romans counted money or count in cardinals? According to this, I should be counting as Avitus recommends:
http://books.google.co.uk/books?id=7FkMAAAAYAAJ&pg=PA437&lpg=PA437&dq=decies+centena&source=bl&ots=mcdYNDwpb4&sig=-sCIpbrWP6h65sxcinGbwxkQ7WE&hl=en&ei=JgQDTN-xL5X80wTu5aX3Ag&sa=X&oi=book_result&ct=result&resnum=5&ved=0CCYQ6AEwBA#v=onepage&q=decies%20centena&f=false but A&G say it's only for money (§138).

Ità verificavi. Recti ut cardinales sunt numeri "centum mīlia", "quīngenta mīlia", "mīliō" (etsi neo-Latinè ultimus), at solùm distributivi atque adverbia numeralia non cardinales illi prolati. Apud A&G (§133) "centum milia" video; in interrete, sicut hîc apud Ciceronem "quīngenta mīlia" (http://www.thelatinlibrary.com/cicero/att3.shtml); et milio apud Morgan (http://facweb.furman.edu/~dmorgan/lexicon/silva.htm) invenitur. Debeone numerare ut Romani quoàd sestertia vel unicè per cardinales? Secundum fontem citatam, pecuniam numerem ut urget Avitus, at secundum A&G (§138) ad pecuniam solam id pertinet.

[Imber Ranae]

And he told me my centum mīlia should be centēna mīlia, not quīngenta mīlia but quīnquiēs centēna mīlia, and not mīliō but deciēs centēna mīlia

I checked and "centum mīlia", "quīngenta mīlia" and "mīliō" are correct as cardinals (the last is neo-Latin, mind you), while "centēna mīlia", "quīnquiēs centēna mīlia", "deciēs centēna mīlia" apply as distributives and numeral adverbs, not cardinals. (See refs. given below.) But should I properly count as the Romans counted money or count in cardinals? According to this, I should be counting as Avitus recommends:
http://books.google.co.uk/books?id=7FkMAAAAYAAJ&pg=PA437&lpg=PA437&dq=decies+centena&source=bl&ots=mcdYNDwpb4&sig=-sCIpbrWP6h65sxcinGbwxkQ7WE&hl=en&ei=JgQDTN-xL5X80wTu5aX3Ag&sa=X&oi=book_result&ct=result&resnum=5&ved=0CCYQ6AEwBA#v=onepage&q=decies%20centena&f=false but A&G say it's only for money (§138).

Ità verificavi. Recti ut cardinales sunt numeri "centum mīlia", "quīngenta mīlia", "mīliō" (etsi neo-Latinè ultimus), at solùm distributivi atque adverbia numeralia non cardinales illi prolati. Apud A&G (§133) "centum milia" video; in interrete, sicut hîc apud Ciceronem "quīngenta mīlia" (http://www.thelatinlibrary.com/cicero/att3.shtml); et milio apud Morgan (http://facweb.furman.edu/~dmorgan/lexicon/silva.htm) invenitur. Debeone numerare ut Romani quoàd sestertia vel unicè per cardinales? Secundum fontem citatam, pecuniam numerem ut urget Avitus, at secundum A&G (§138) ad pecuniam solam id pertinet.

There's some confusion here. I haven't watched your video and so don't know exactly what the context is, but centum milia and quingenta milia are definitely the correct cardinals for 100,000 and 500,000 respectively (distributives would be centena milia and quingena milia respectively). However decies centena milia, classical Latin for one million, can act both as a cardinal and as a distributive. This indistinguishability is a simple side-affect of the way multiplication is represented in Latin, namely the regular use of distributive numerals, instead of cardinals, with numeral adverbs (though this isn't the case with representations of small numbers in poetry by multiplication, e.g. bis septem for quattuordecim).

Furthermore I think you've misread A&G, who say only that the use of such large numbers was for the Romans mostly limited to the reckoning of money, meaning they rarely had to deal with anything that could reach such astronomical sums outside of the commercial realm. This has nothing to do with a distinction between normal and monetary reckoning of quantities. And because they lacked the convenient neo-Latin numeral milio, the Romans had to resort to the impractical method of multiplication to express numbers equal to one million or higher (I'm guessing mille milia was deemed too awkward). This was achieved by simply multiplying the previous order (converted to distributives) by the desired numeral adverb.

I believe quinquies centena milia, though theoretically possible, would have been felt a superfluous variant of the entirely viable quingenta milia.

[adrianus]

"...meaning they rarely had to deal with anything that could reach such astronomical sums outside of the commercial realm."

That's not the case. Don't Romans talk about 10000, 50000, 100000, 500000 soldiers, people, and paces, among other things?
Minimè. Nonnè assuetissimi Romanis ut numeri hominum atque milituum passuumque inter alia sunt decem milia, quinquaginta milia, centum milia, quingenta milia?

I'm guessing mille milia was deemed too awkward

Not for Priscian, anyway. He uses it. Priscianus (De Figuris Numerorum, liber primus, §§7,8, Keil III, p.407) says decem milia, quinquaginta milia, centum milia, quingenta milia, mille milia.

Priscianus est unus qui mille milia (secùs decem milia, quinquaginta milia, centum milia, quingenta milia) in libro suo De Figuris Numerorum scripsit.

[adrianus]

I looked at this book of Gerbert of Aurillac's writings, where I found his explanation of how to use an abacus. It's just great, I think (if you like numbers!).
In hôc volumine operum Gerberti quaesivi in quo modus enumerandi per abacum tractatur, ut feliciter inveni. Quam magna est haec fons, ut credo (si numeri tibi placent)!

N. Bubnov (ed.), Gerberti postea Silvestri II papae Opera Mathematica (972-1003), Berolini 1899 (http://www.archive.org/details/gerbertiposteas00sylvgoog)

Nam sicut unitas significat X in decenis et C in centenis, sic etiam mille in millenis et decem millia in decenis millenis, nec non centum millia in centenis millenis. Binarius vero, quomodo XX in decenis et CC in centenis, sic etiam duo millia in millenis, et XX millia in decenis millenis, et ducenta millia in centenis millenis, et cetera ad hunc modum.

For just as one signifies 10 in the 10s [column] and 100 in the 100s, so too 1000 in the 1000s and 10000 in the 10000s, as too 100000 in the 100000s. Two of course, just as 20 in the 10s and 200 in the 100s, so also means 2000 in the 1000s, 20000 in the 10000s and 200000 in the 100000s and so on in this way.

"A one" = "unitas"; "a two" = "binarius"; "a three" = "ternarius"; "a four" = "quaternarius"; "a five" = "quinarius"; "senarius" = "a six"; "a seven" = "septenarius"; "an eight" = "octonarius"; "a nine" = "novenarius".

To count in tens, in hundreds, in thousands is "In decenis, in centenis, in millenis numerare".

Then "decem millia" (10000), "centum millia" (100000), "mille millia" (1000000), "decies mille millia" (10000000) [at non decem mille millia, quia singulis numeri est mille], "centies mille millia" (100000000), "millies mille millia" (1000000000), "decies millies mille millia" (10000000000), "centies millies mille millia" (100000000000), "mille millies mille millia" (1000000000000), "decies mille millies mille millia" (10000000000000) and so on // et caetera!

Here is Pliny the Elder:

Non erat apud antiquos numerus ultra centum milia; itaque et hodie multiplicantur haec, ut decies centena aut saepius dicantur.

But here is Livy:

Carthaginienses tritici modium sexcenta [600000], hordei quingenta milia [500000] ad exercitum, dimidium eius Romam apportaturos polliciti sunt: id ut ab se munus Romani acciperent, petere sese. et classein [suorum] suo sumptu comparaturos; et stipendium, quod pluribus pensionibus in multos annos deberent, praesens omne daturos. Masinissae legati quingenta milia [500000] modium tritici, trecenta [300000] hordei ad exercitum in Graeciam, Romam trecenta milia [300000] modium tritici, ducenta quinquaginta [250000] hordei ; equites quingentos , elephantos viginti regem ad M. Acilium consulem missurum.

[Imber Ranae]

That's not the case. Don't Romans talk about 10000, 50000, 100000, 500000 soldiers, people, and paces, among other things?

Now you're misreading me as well as A&G. They, and I, are referring specifically to numbers one million and greater. These are the numerals which require the use of multiplication in classical Latin.

Numeral Adverbs are used with mille to express the higher numbers:

ter et trīciēns (centēna mīlia) sēstertium, 3,300,000 sesterces (three and thirty times a hundred thousand sesterces).
vīciēs ac septiēs mīliēs (centēna mīlia) sēstertium, 2,700,000,000 sesterces (twenty-seven thousand times a hundred thousand).

Note.--These large numbers are used almost exclusively in reckoning money, and centena milia is regularly omitted."

Granted, it's not explicitly explained (a problem I've found with A&G in general) what "the higher numbers" refers to, so your confusion is understandable. But it's clear from the context: Notice that the earlier list of cardinals only goes through 100,000 (centum mīlia). Some of the other grammars explain this much better, and actually include one million in their tables.

[It's also only with sestertium that centena milia is regularly omitted]

Not for Priscian, anyway. He uses it. Priscianus (De Figuris Numerorum, liber primus, §§7,8, Keil III, p.407) says decem milia, quinquaginta milia, centum milia, quingenta milia, mille milia.

Priscianus est unus qui mille milia (secùs decem milia, quinquaginta milia, centum milia, quingenta milia) in libro suo De Figuris Numerorum scripsit.

Well of course you're going to have some variations in usage over the hundreds of years of a language's lifetime. Regardless, [numeral adverb] + centena milia is far and away the most common way of expressing the millions and above in Latin, and not just for sesterces. Check for yourself if you don't believe me.

[adrianus]

Now you're misreading me as well as A&G. They, and I, are referring specifically to numbers one million and greater. These are the numerals which require the use of multiplication in classical Latin.

I get that. But for me, Imber Ranae, from the beginning, this has been about numbers (or parts of numbers) between 100000 and 1000000, where the criticism that "centum mīlia should be centēna mīlia, not quīngenta mīlia but quīnquiēs centēna mīlia, and not mīliō but deciēs centēna mīlia" could possibly be based on the Pliny quote. And isn't the stuff in the Gerbert book interesting about how to mix adverbials and cardinals for very big numbers.

What a great tool, Imber Ranae. I didn't know it before. http://monumenta.ch/latein/index.php?lang=0

Id intellego. Tuâ veniâ, Imber Ranae, res mihi ab initio numeros (vel partes eorum) inter centum milia et mille millia (seu milio seu decies centena milia) spectat et vis verborum Plinii in eo spatio excaecet. Nonnè attractivè liber Gerberti suprà citatus illuminat quomodo adverbi et cardinales inter se in numeris ingentis magnitudinis misceantur.

Quam mirum hoc instrumentum! http://monumenta.ch/latein/index.php?lang=0 Id adhûc ignoravi.

Addendum
Here's Cicero, BTW, with "mille...milia"

Dedi stipendio, frumento, legatis, pro quaestore, cohorti praetoriae hs mille sescenta triginta quinque milia quadringentos decem et septem nummos [1,635,417 sesterces].

And with 1,800,000 sesterces

Quod minus Dolabella Verri acceptum rettulit quam Verres illi expensum tulerit quingenta triginta quinque milia, et quod plus feci labella Verrem accepisse quam iste in suis tabulis habuit HS ducenta triginta duo milia, et quod plus frumenti fecit accepisse istum, HS deciens et octingenta milia [1,800,000,—non octingena, nota], tu homo castissimus aliud in tabulis habebas. Hinc extraordinariae pecuniae, quas nullo duce tamen a ex particula investigamus, redundarunt, hinc ratio Q. et Cn. Postumis Curtiis multis nominibus, quorum in tabulis iste habet nullum; hinc HS quater deciens [quater deciens centena milia = 1,400,000] P. Tadio numeratum Athenis testibus planum faciam.

and Vitruvius

Si autem animadverterint orbis terrae circumitionem per solis cursum et umbras gnomonis aequinoctialis ex inclinatione caeli ab Eratosthene Cyrenaeo rationibus mathematicis et geometricis methodis esse inventam ducentorum quinquaginta duum milium stadium, quae fiunt passus trecenties et decies quinquies centena milia, huius autem octava pars, quam ventus tenere videtur, est triciens nongenta triginta septem milia et passus quingenti, non debebunt mirari, si in tam magno spatio unus ventus vagando inclinationibus et recessionibus varietates mutatione flatus faciat.